An air cooling system for a jet plane operates on simple air cycle. The cockpit is to be maintained at 20°C The ambient air pressure and temperature are 0.9 kgf /cm2 and 32°C. Calculate the stagnation pressure of the air entering the first stage of the main compressor if the ram efficiency is assumed as 80 per cent with the plane speed of 1000 km / hr. Main compressor pressure ratio is 3. Stagnation temperature of the air entering the cooling turbine is 85°C. Pressure drop through heat exchanger is 0.2 kgf / cm2. Compressor and turbine adiabatic efficiencies are 80 per cent. Pressure in the cockpit is 1 kgf / cm2. The pressure of the air leaving the cooling turbine is 1.1 kgf / cm2. Cockpit cooling load is 1 tonne. Neglect frictional losses and assume that the air is dry and behaves as a perfect gas with g = 1.4. Determine:
(a) the stagnation temperature of the air entering and leaving the compressor.
(b) the temperature of the air leaving the cooling turbine.
(c) the rate of air flow.
(d) the coefficient of performance of the cycle.